The term 'wrapper' gets thrown around a lot. Generally its used to describe a class which contains an instance of another class, but which does not directly expose that instance. The wrapper's main purpose is to provide a 'different' way to use wrapped object (perhaps the wrapper provides a simpler interface, or adds some functionality).
The word 'wrapper' can also be used when describing classic design patterns.
Wrapping an object to provide a simplified interface to it is often described as the 'Facade' pattern. The wrapper is the facade.
Sometimes you may have a class which would suit a specific interface, but you can't change the code for it to make it conform to that interface. You can create a wrapper for that class which implements the interface, but which directs most of the calls to the wrapped object. This is the 'Adapter' pattern. The wrapper is the adapter.
The instance you describe, where you have two classes which can do array sorting using different algorithms sounds like the 'Strategy' pattern, where you provide a way to perform an operation on some object, but the algorithm used for that operation may be different depending upon the structure of that object.
For example, one of your sort algorithms may be great for arrays of length less than 100, but then performance might be an issue for it. The other algorithm might be good for bigger arrays. You can create a 'wrapper' for the two algorithms which supports the sort operation but decides which algorithm to use based on the array length.
The vast majority of wrappers exist to hide some sort of complexity.